Dynamics of a rectangular thin plate with lumped mass under harmonic foundation and in‐plane excitations,ZAMM - Journal of Applied Mathematics and Mechanics

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Dynamics of a rectangular thin plate with lumped mass under harmonic foundation and in‐plane excitations
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-09-22 , DOI: 10.1002/zamm.202000216
Liangqiang Zhou ₁ , Peng Ji ₁ , Fangqi Chen ₁

Affiliation

Nonlinear dynamic behaviors including global bifurcations and multi‐pulse chaotic dynamics of a rectangular thin plate with lumped mass subjected to a harmonic foundation excitation and in‐plane excitation are investigated in this paper. With the von K

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n equation and Galerkin method, the dynamic equation of the first two modes for this model is obtained. Utilized the method of multiple scales, the average equation of the system in the case of both primary resonance and 1/2 subharmonic resonance is obtained. Global bifurcations and chaotic dynamics of the rectangular thin plate are analyzed with the energy‐phase method. The effect of the dissipation factor on pulse sequence and layer radius is discussed in detail. The results obtained here indicate that there exist Silnikov‐type multi‐pulse orbits homoclinic to certain invariant sets for the resonant case, which means that chaotic motion may occur. Homoclinic trees describing the repeated bifurcations of multi‐pulse solutions are also obtained. With the Runge–Kutta method, numerical simulations including the time histories and phase portraits are given, which demonstrate that chaotic behaviors may occur and confirm the analytical results.

中文翻译：

谐波基础和面内激励作用下具有集中质量的矩形薄板的动力学

本文研究了具有集中质量的矩形薄板在谐波基础激励和面内激励作用下的非线性动力学行为，包括整体分叉和多脉冲混沌动力学。与冯·K

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R M

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利用n方程和Galerkin方法，得到了该模型的前两种模式的动力学方程。利用多尺度法，获得了系统在一次共振和1/2次谐波共振情况下的平均方程。用能量相方法分析了矩形薄板的整体分叉和混沌动力学。详细讨论了耗散因数对脉冲序列和层半径的影响。此处获得的结果表明，对于共振情况，存在与某些不变集同向的Silnikov型多脉冲轨道，这意味着可能会发生混沌运动。还获得了描述多脉冲解的重复分支的同宿树。使用Runge–Kutta方法，

更新日期：2020-09-22

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